Method for detecting targets using space-time adaptive processing and shared knowledge of the environment

ABSTRACT

A method detects a target in a radar signal using space-time adaptive processing. A test statistic is 
               T   =         max   α     ⁢       max   λ     ⁢       ∫   R     ⁢         f   1     ⁡     (       x   0     ,     x   1     ,   …   ⁢           ,       x   K     ❘   α     ,   λ   ,   R     )       ⁢     p   ⁡     (   R   )       ⁢           ⁢     ⅆ   R                 max   λ     ⁢       ∫   R     ⁢         f   0     ⁡     (       x   0     ,     x   1     ,   …   ⁢           ,       x   K     ❘   λ     ,   R     )       ⁢     p   ⁡     (   R   )       ⁢           ⁢     ⅆ   R               ,         
where x 0  is a test signal, x k  are K training signals, α is an unknown amplitude of a target signal within the test signal, λ is a scaling factor, R is a covariance matrix of the training signals, and a function max returns a maximum values. The test statistic is compared to a threshold to determine whether the target is present, or not.

FIELD OF THE INVENTION

This invention relates generally to signal processing, and in particularto space-time adaptive processing (STAP) for target detection usingradar signals.

BACKGROUND OF THE INVENTION

Space-time adaptive processing (STAP) is frequently used in radarsystems to detect a target. STAP has been known since the early 1970's.In airborne radar systems, STAP improves target detection wheninterference in an environment, e.g., ground clutter and jamming, is aproblem. STAP can achieve order-of-magnitude sensitivity improvements intarget detection.

Typically, STAP involves a two-dimensional filtering technique appliedto signals acquired by a phased-array antenna with multiple spatialchannels. Coupling the multiple spatial channels with time dependentpulse-Doppler waveforms leads to STAP. By applying statistics ofinterference of the environment, a space-time adaptive weight vector isformed. Then, the weight vector is applied to the coherent signalsreceived by the radar to detect the target.

FIG. 1 shows the signal model of the conventional STAP. When no targetis detected, acquired signals 101 include a test signal x₀ 110consisting of the disturbance d₀ 111 only, and a set of training signalsx_(k), k=1, 2, . . . , K, 120, which are independent and identicallydistributed (i.i.d.) with the disturbance d₀ 111. When a target isdetected, acquired signals 102 include the test signal 110 consisting ofa target signal and the disturbance d₀ 111, and a set of i.i.d. trainingsignals x_(k) 120 with respect to d₀ 111. The target signal can beexpressed as a product of a known steering vector s 130 and an unknownamplitude α.

As shown in FIG. 2 for conventional target detection with STAP, twotypes of the estimation sources of the disturbance covariance matrix areusually used for a homogeneous environment where the covariance matrixof the test signal 110 is the same as that of the training signal 120.These two methods are the estimation of disturbance covariance matrix220 from training signals 120 via a covariance matrix estimator 210, andthe generation of the disturbance covariance matrix 250 from priorknowledge 230 via a covariance matrix generator 240. The knowledgedatabase can include maps of the environment, past measurements, etc.

As shown in FIG. 3, a conventional method, known as Kelly's generalizedlikelihood ratio test (GLRT), takes the acquired signals including thetest signal 110 and training signals 120 as input, and then determinesthe ratio 330 of

$\begin{matrix}{\max\limits_{\alpha}{\max\limits_{R}{{f_{1}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\alpha},R} \right)}\mspace{14mu}{and}}}} & 310 \\{{\max\limits_{R}{f_{0}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘R}} \right)}},} & 320\end{matrix}$

where α is the amplitude of the target signal, x_(k) are target freetraining signals, x₀ is the test signal, R is the covariance matrix ofthe training signals, and ƒ₁( ) and ƒ₀( ) are likelihood functions undertwo hypothesis H₁, i.e., the target is present in the test signal, andH₀, i.e., the target is not present in the test signal, respectively.The resulting test statistic 340 is compared to a threshold 350 todetect 360 the target.

FIG. 5 shows a conventional Bayesian treatment for the detection problemin a homogeneous environment, which assumes the disturbance covariancematrix is randomly distributed with some prior probability distribution.

Inputs are the test signal 110, the training signals 120 and a knowledgedatabase 230. The resulting detectors are often referred to as theknowledge aided (KA) detectors for the homogeneous environment. Thedetector determines the ratio 530 of

$\begin{matrix}{\max\limits_{\alpha}{\int\limits_{R}{{f_{1}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\alpha},R} \right)}{p(R)}\ {\mathbb{d}R}\mspace{14mu}{and}}}} & 510 \\{\int\limits_{R}{{f_{0}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘R}} \right)}{p(R)}\ {{\mathbb{d}R}.}}} & 520\end{matrix}$

The resulting test statistic T 540 is compared to a threshold 550 todetect 560 whether a target is present, or not.

For non-homogeneous environments, several models are known. One model isthe well-known compound-Gaussian model, in which the training signal isa product of a scalar texture, and a Gaussian vector. The texture isused to simulate power oscillations among the signals.

Another model is the partially homogeneous environment, by which thetraining signals 120 share the covariance matrix with the test signal110 up to an unknown scaling factor X.

FIG. 4 shows a conventional GLRT treatment on the detection problem,which results in the well-known adaptive coherence estimator (ACE) forthe partially homogeneous environment. In that method, the inputincludes the acquired signals 101 comprising the test 110 and trainingsignals 120. Then, the ratio 430 of

$\begin{matrix}{{\max\limits_{\alpha}{\max\limits_{\lambda}{\max\limits_{R}{f_{1}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\alpha},\lambda,R} \right)}}}}\;,{and}} & 410 \\{\max\limits_{\lambda}{\max\limits_{R}{f_{0}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\lambda},R} \right)}}} & 420\end{matrix}$is determined, where α is amplitude of the test signal, x_(k) are targetfree training signals, x₀ is the test signal, R is the covariancematrix, ƒ₁( ) and ƒ₀( ) are the likelihood functions under twohypothesis H₁, i.e., the target is present in the test signal, and H₀,i.e., the target is not present in the test signal. The resulting teststatistic 440 is compared to a threshold 450 to detect 460 the presenceof a target.

SUMMARY OF THE INVENTION

The embodiments of the invention provide a method for detecting targetsin radar signals using space-time adaptive processing (STAP). Differentfrom the conventional partially homogeneous model, a stochasticpartially homogeneous model is used by the embodiments of the invention,which incorporate some a priori knowledge to the partially homogeneousmodel. The stochastic partially homogeneous retains the powerheterogeneity between the test signal and the training signals with anadditional power scaling factor.

In this invention, according to the stochastic partially homogeneousmodel, the scale invariant generalized likelihood ratio test isdeveloped from using Bayesian framework.

Accordingly, a likelihood function is integrated over a priorprobability distribution of the covariance matrix to obtain anintegrated likelihood function. Then, the integrated likelihood functionis maximized with respect to deterministic but unknown parameters, ascaling factor A and a signal amplitude α.

Finally, an integrated generalized likelihood ratio test (GLRT) isderived in a closed-form. The resulting scale-invariant GLRT is aknowledge-aided (KA) version of an adaptive coherence estimator (ACE).

Specifically, our KA-ACE uses a linear combination of the samplecovariance matrix and the a priori matrix R as its weighting matrix. Theloading factor of R is linear with respect to the parameter μ, whichreflects the accuracy of the priori matrix R.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of prior art signals when a target is presentor not;

FIG. 2 is a block diagram of prior art covariances matrix estimates ofbackground clutter from training signals and from a knowledge databasevia the estimates;

FIG. 3 is a block diagram of prior art generalized likelihood ratio test(GRLT) for homogeneous environments in the prior art;

FIG. 4 is a block diagram of prior art GLRT for partially homogeneousenvironments, referred to as adaptive coherence estimator (ACE);

FIG. 5 is a block diagram of prior art knowledge aided GLRT forstochastic homogeneous environments; and

FIG. 6 is a block diagram of knowledge aided ACE for stochasticpartially homogeneous environments according to embodiments of theinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As shown in FIG. 6, the embodiments of the invention provide a methodfor detecting targets using space-time adaptive processing (STAP) oftest signals, and a generalized likelihood ratio test (GLRT). Ourscale-invariant GLRT is a knowledge-aided (KA) version of an adaptivecoherence estimator (ACE). The steps of the method can be performed in aprocessor 600 connected to a memory and input/output interfaces as knownin the art.

Specifically, we use the following hypothesis testing problem:H ₀ :x ₀ =d ₀ , x _(k) =d _(k) , k=1, . . . , K,H ₁ :x ₀ =αs+d ₀ , x _(k) =d _(k) , k=1, . . . , K,  (1)where the hypothesis H₀ is that the target is not present in the testsignal, H₁, the target is present in the test signal, x_(k) are targetfree training signals 120, x₀ is the test signal 110, s is an array of apresumed known response, α is an unknown complex-valued amplitude of thetest signal, and d₀ and d_(k) are the disturbance covariance matrices R₀and R of the test and training signals, respectively.

The covariance matrix R of the training signals is random and has aprobability density function p(R), which is a function of the covariancematrix prior probability matrix R.

A test statistic T 630 is determined from a Bayesian framework accordingto Equation (2), a ratio 330 of 610 to 620, and a scaling factor λ

$\begin{matrix}{{T = \frac{\max\limits_{\alpha}{\max\limits_{\lambda}{\int\limits_{R}{{f_{1}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\alpha},\lambda,R} \right)}{p(R)}\ {\mathbb{d}R}}}}}{\max\limits_{\lambda}{\int\limits_{R}{{f_{0}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\lambda},R} \right)}{p(R)}\ {\mathbb{d}R}}}}},} & (2)\end{matrix}$wherein a function max returns a maximum value, and λ can be in a rangeof about [1-16].

The GRLT in Equation (2) can be reduced to

$\begin{matrix}{{T = \frac{\max\limits_{\alpha}{\max\limits_{\lambda}{\lambda^{- N}{{\overset{-}{\Sigma}}_{1}}^{- L}}}}{\max\limits_{\lambda}{\lambda^{- N}{{\overset{-}{\Sigma}}_{0}}^{- L}}}},} & (3)\end{matrix}$where L=K+μ+1, andΣ _(i)=τ_(i)+(μ−N) R=λ ⁻¹ y _(i) y _(i) ^(H) +S+(μ−N) Rwithy _(i) =x ₀−β_(i) αs,β ₁=1, β₀=0,and

$S = {\sum\limits_{k = 1}^{K}{x_{k}{x_{k}^{H}.}}}$

After deriving and substituting the maximum likelihood estimate of thescalar λ into Equation (3), the our test statistics T becomes

$\begin{matrix}{T = {{\max\limits_{\alpha}\frac{{\hat{\lambda}}_{{ML},0}^{N}{{{\overset{-}{\Sigma}}_{0}\left( {\hat{\lambda}}_{{ML},0} \right)}}^{L}}{{\hat{\lambda}}_{{ML},1}^{N}{{{\overset{-}{\Sigma}}_{1}\left( {\alpha,{\hat{\lambda}}_{{ML},1}} \right)}}^{L}}} = {\left\lbrack \frac{x_{0}^{H}\Gamma^{- 1}x_{0}}{\min\limits_{\alpha}{\left( {x_{0} - {\alpha\; s}} \right)^{H}{\Gamma^{- 1}\left( {x_{0} - {\alpha\; s}} \right)}}} \right\rbrack^{N}.}}} & (4)\end{matrix}$

Next, the amplitude α in Equation (4) is replaced by a maximumlikelihood estimate of the amplitude α according to

$\begin{matrix}{{\hat{\alpha}}_{ML} = {\frac{s^{H}\Gamma^{- 1}x_{0}}{s^{H}\Gamma^{- 1}s}.}} & (5)\end{matrix}$

Taking the N^(th) square root of Equation (4) and using monotonicproperties of the function ƒ(x)=1/(1−x), the new test statistic 630 is

$\begin{matrix}{T_{{KA}\text{-}{ACE}} = {\frac{{{s^{H}\Gamma^{- 1}x_{0}}}^{2}}{\left( {s^{H}\Gamma^{- 1}s} \right)\left( {x_{0}^{H}\Gamma^{- 1}x_{0}} \right)}\overset{H_{1}}{\underset{H_{0}}{\gtrless}}\gamma_{{KA}\text{-}{ACE}}}} & (6)\end{matrix}$where γKA-ACE denotes a threshold subject to a probability of a falsealarm.

The KA-ACE for the stochastic partially homogeneous environment takesthe form of the standard ACE, except that the whitening matrix is

$\begin{matrix}{{\Gamma = {{S + {\left( {\mu - N} \right)\overset{-}{R}}} = {{\sum\limits_{k = 1}^{K}{x_{k}x_{k}^{H}}} + {\left( {\mu - N} \right)\overset{-}{R}}}}},} & (7)\end{matrix}$which uses a linear combination between the sample covariance matrix Sand the prior knowledge covariance matrix R. The weighting factor of theprior knowledge is controlled by μ. It makes sense that the KA-ACE putsmore weights on the prior matrix R, when the prior matrix is moreaccurate, i.e., μ is relatively large.

In comparison, the conventional ACE also takes the same form, but withthe whitening matrix given by the sample covariance matrix=Γ=S. Thestatistic is finally compared to a threshold 350 to detect 360 whether atarget signal 130 is present in the test signal 110.

Effect of the Invention

The embodiments of the invention provide a method for detecting targets.A knowledge-aided adaptive coherence estimator ACE is provided for astochastic partially homogeneous environment, which models the poweroscillation between the test and the training signals and treats thedisturbance covariance matrix as a random matrix.

The KA-ACE has a color-loading form between the sample covariance matrixand the prior knowledge used for the whitening matrix. We note that theKA-ACE is scale invariant and performs better than the conventional ACEin various applications.

Although the invention has been described by way of exes of preferredembodiments, it is to be understood that various other adaptations andmodifications may be made within the spirit and scope of the invention.Therefore, it is the object of the appended claims to cover all suchvariations and modifications as come within the true spirit and scope ofthe invention.

We claim:
 1. A method for detecting a target in a radar signal usingspace-time adaptive processing, comprising the steps: using anelectronic processor for determining a test statistic${T = \frac{\max\limits_{\alpha}{\max\limits_{\lambda}{\int\limits_{R}{{f_{1}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\alpha},\lambda,R} \right)}{p(R)}\ {\mathbb{d}R}}}}}{\max\limits_{\lambda}{\int\limits_{R}{{f_{0}\left( {x_{0},x_{1},\ldots\mspace{14mu},{x_{K}❘\lambda},R} \right)}{p(R)}\ {\mathbb{d}R}}}}},$where x₀ is a test signal, x_(k) are K training signals, α is an unknownamplitude of a target signal within the test signal, λ is a scalingfactor, R is a covariance matrix of the training signals, and a functionmax returns a maximum values; and comparing the test statistic to athreshold to determine whether the target is present, or not.
 2. Themethod of claim 1, wherein a hypothesis testing problem is used asfollowsH ₀ :x ₀ =d ₀ , x _(k) =d _(k) , k=1, . . . , K,H ₁ :x ₀ =aαs+d ₀ , x _(k) d _(k) , k=1, . . . , K, where a hypothesisH₀ is that the target is not present in the test signal, a hypothesis H₁is that the target is present in the test signal, and d₀ and d_(k) arenoise terms for covariance matrices of the test signal and trainingsignals, respectively.
 3. The method of claim 1, wherein the covariancematrix R is random and has a probability density function p(R), which isa function of a covariance matrix prior probability matrix R.
 4. Themethod of claim 1, further comprising: replacing the unknown amplitude αby a maximum likelihood estimate of the amplitude α.